There are flash carts for the DS like the DsTwo. It's a custom-made DS cartridge with a slot for a microSD card, which is where you put the OS of the flash cart

There are flash carts for the DS like the DsTwo. It's a custom-made DS cartridge with a slot for a microSD card, which is where you put the OS of the flash cart along with any roms/software to run with it. Getting one for the old DS/DSi line is a safe bet because their firmware isn't updated anymore. Firmware updates are liable to brick flash carts.